Monty Hall was a Canadian game show host who would offer the contestants 3 doors. One of the door would have a luxury car behind it while the other two had goats. Contestant would obviously want to open the door with a car behind it instead of a goat.
Varaible Change in Statistics helps in solving this Monty Hall problem. This problem calls for you to not consider your emotions and only use logic like all problems in Maths and Statistics.
So what emotions am I talking about. I’m talking about emotions of greed, impatient and selfishness. If you’re able to put a lid on these emotions and not act on them, this problem is easy to solve with logic. As mentioned, host will ask the contestant to pick a door out of 3 doors, once you pick a door, say door#2, Host will open another door say door#1 to show there’s a goat behind the door.
Now he will gives the contestant an option to either to stay with their earlier choice i.e. door no. 2 or switch to door no. 3. Now as a contestant you might think there is 50% chance that you might win or lose. But that isn’t the case, let’s understand how.
When you are offered 3 doors, you have 1/3 chance with door you picked (i.e. door 2) , i.e. 33% chance to win the car.
Now that means the other 2 doors, i.e. door 1 and door 3 have 2/3rd or 66.67% chance they have the car in them. Now, Monty Hall would open door 1 to show you that there’s a goat behind it. The host will now ask you to either switch or stay with the door selected earlier.(i.e. door 2)
Well, according to variable change one should always switch, since both door 1 and door 3 had 2/3rd chance of winning and once door 1 was revealed to have a goat behind it. Door 3 automatically becomes more preferable as door 1 has 33.33% chance of winning while door 3 now has 66.67% chance of winning.
A contestant is faced with a 50% chance of winning is actually an illusion. He/ She is faced with a 66.67% chance of winning. Hence, as a contestant one should always switch as it increases the chances of winning.
Written by: Ms. Gitika Chandra